AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 13.3 Multicollinearity

Multicollinearity occurs when two or more independent variables in a regression model are highly correlated to each other Standard error of the OLS parameter estimate will be higher if the corresponding independent variable is more highly correlated to the other independent variables in the model

Multicollinearity Independent variables show no statistical significance when conducting the basic significance test It is not a mistake in the model specification, but due to the nature of the data at hand

Perfect Multicollinearity Perfect multicollinearity occurs when there is a perfect linear correlation between two or more independent variables When independent variable takes a constant value in all observations

Severe Multicollinearity The OLS method cannot produce parameter estimates A certain degree of correlation (multicollinearity) between the independent variables is normal and expected in most cases Severe multicollinearity

Symptoms of Multicollinearity The symptoms of a multicollinearity problem 1. independent variable(s) considered critical in explaining the model’s dependent variable are not statistically significant according to the tests

Symptoms of Multicollinearity 2.High R 2, highly significant F-test, but few or no statistically significant t tests 3.Parameter estimates drastically change values and become statistically significant when excluding some independent variables from the regression

Detecting Multicollinearity A simple test for multicollinearity is to conduct “artificial” regressions between each independent variable (as the “dependent” variable) and the remaining independent variables Variance Inflation Factors (VIF j ) are calculated as:

Detecting Multicollinearity VIF j = 2, for example, means that variance is twice what it would be if X j, was not affected by multicollinearity A VIF j >10 is clear evidence that the estimation of B j is being affected by multicollinearity

Addressing Multicollinearity Although it is useful to be aware of the presence of multicollinearity, it is not easy to remedy severe (non-perfect) multicollinearity If possible, adding observations or taking a new sample might help lessen multicollinearity

Addressing Multicollinearity Exclude the independent variables that appear to be causing the problem Modifying the model specification sometimes help, for example:  using real instead of nominal economic data  using a reciprocal instead of a polynomial specification on a given independent variable